A layman's take:
Maybe the antibodies are different because the immune system is being presented with _only_ the spike protein, rather than the whole virus?
From my understanding, the immune system breaks the viral proteins up into pieces and then starts rapidly "evolving" antibodies to target those pieces. The goal being to ultimately produce antibodies that target those pieces, and don't target the learned whitelist of proteins (from your own body). Once it's got that it begins deploying antibody producing cells, and remembers the antibodies for later infections.
What I'm curious about is the stopping criteria the body uses during the evolution stage. It sounds like it's producing an array of antibodies, not just one kind. So the stopping criteria isn't finding one working antibody. Perhaps it's more like, "Produce at least N different antibodies."
If the latter, then the difference between natural and mRNA immunity makes sense to me. If your immune system is working to produce N different antibodies for the whole viral proteome, less of those antibodies will target the spike protein. And thus it will have less resilience to changes in the spike protein. But of course more tolerance to changes in the virus as a whole. Whereas with mRNA the immune system only sees the spike proteins, and since it's still going to make N different antibodies it'll have more tolerance for changes to the spike protein.
What's most interesting to me, assuming any of the above is close to reality, is that mRNA vaccines allow us to give our immune system an inductive bias of some kind. Presumably our immune systems aren't "smart" enough to know what parts of a virus are most conserved, and thus best to target. It just targets all of it blindly. mRNA vaccines used the spike protein because we believe that to be the most conserved proteins. If those change too much the virus either won't work, or will effectively be a different species. So our mRNA vaccines are a way of telling our immune systems to focus their work on the "important" proteins, and thus, we would assume, give us better immunity.
Whether our guess about the spike proteins is correct remains to be seen I suppose.